Extracting a symbolic variable (rearranging symbolic equation)

Hi,

I am trying to extract a variable (a gain in this case) from a symbolic expression.

The code for generating the symbolic expression is:

%Misc Intializations
syms K2 K1 s

%Plant characteristics
T=.1;
Wn=2.5;
z=.3;

%Controller
C=K2*expand((s+2)^2)/expand((s+10)*(s+100));
%Actuator
A=10/(s+10);
%Plant
P=K1*(T*s+1)/(s^2+2*Wn*z*s+Wn^2);

%Closed Loop TF
YcY=C*A*P/(1+C*A*P);

%Characteristic
KLs=expand(C*A*P);

Where the expression I want to work with is KLs, which in its current form is:

4*K1*K2*s^3 + 56*K1*K2*s^2 + 176*K1*K2*s + 160*K1*K2
----------------------------------------------------------
4*s^5 + 486*s^4 + 9145*s^3 + 55600*s^2 + 112500*s + 250000

I want to bring K1 and K2 outside the expression (make them into gains for the transfer function). In this case it is relatively simple to do so using coeffs however I need a method that will work when K1,K2...Kn can be in the numerator or the denominator.

Not sure if what I am asking is clear but thank you in advance for help!

[Mech Princess]

Did you find a solution for this? I am trying to do something similar for another application. I am trying to have K1 on one side of equation and have all variables on the other side. is that possible? Thanks

Answer 1

[Walter Roberson]

factor() might help.

Answer 2

[Aider]

Try this, create a dummy variable "x" so you can use the collect command. Then substitute x by K1*K2

%Misc Intializations
syms K2 K1 s x
%Plant characteristics
T=.1;
Wn=2.5;
z=.3;
%Controller
C=K2*expand((s+2)^2)/expand((s+10)*(s+100));
%Actuator
A=10/(s+10);
%Plant
P=K1*(T*s+1)/(s^2+2*Wn*z*s+Wn^2);
%Closed Loop TF
YcY=C*A*P/(1+C*A*P);
%Characteristic
KLs=expand(C*A*P);
subs(collect(subs(KLs,K1*K2,x),x),x,K1*K2)